On 22/04/16 18:49, Colin Cotter wrote:
> OK, are you trying to match an analytical solution?
>
> I think it depends on whether you integrated by parts in the grad term,
> or the divergence. If you integrated by parts in the grad term, then you
> can get the 0 pressure boundary condition naturally i.e. without setting
> anything.
>
> all the best
> --cjc

To add to that, the natural ("do nothing") boundary condition leads to a
zero stress condition. This is I think also where the difference between
including and excluding the grad-div term comes from. The tangential
component of stress is different (dv/dx vs. dv/dx+du/dy) and is not
sufficiently constrained by the boundary conditions. If you include the
grad-div term the tangential stress is non-zero and so you either have
to explicitly add that as a boundary term to weakly enforce the correct
value of dv/dx+du/dy, or you apply a strong dirichlet on the tangential
component of velocity. Without the grad-div term the "do-nothing" bc for
the tangential stress automatically enforces dv/dx=0.

Cheers
Stephan

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